For the given hemispherical shell,the direction of the gravitational intensity at an arbitrary point $P$ on its rim is indicated by which arrow?

Gravitational potential in a region is given by $V = -(x + y + z) \text{ J/kg}$. Find the gravitational intensity at $(2, 2, 2)$ in $\text{N/kg}$.

$A$ sphere of mass $M$ and radius $R_2$ has a concentric cavity of radius $R_1$ as shown in the figure. The force $F$ exerted by the sphere on a particle of mass $m$ located at a distance $r$ from the center of the sphere varies as $(0 \le r \le \infty)$. Which of the following graphs correctly represents this variation?

What is the relationship between gravitational field intensity $(I)$ and gravitational potential $(V)$ at a point?

The mass of the Earth is $81$ times the mass of the Moon and the distance between their centres is $R$. The distance from the centre of the Earth where the gravitational force will be zero is

Two identical heavy spheres are separated by a distance $10$ times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.